Sucking on a thumb or finger is a completely normal habit that some babies develop even before they're born. It's soothing, and it also helps babies make contact with and explore their environment. If sucking habits go on much past the age of 3, however, it's possible that bite problems may arise.
In a normal bite, the upper teeth grow to overlap the lower teeth. But it's possible for the pressure of a thumb, finger or pacifier resting on the gums to interfere with normal tooth eruption and even jaw growth. Some thumb-suckers develop an “open bite,” meaning the teeth don't overlap when a child bites together; instead, there is an open space between the upper and lower teeth. That's why thumb sucking is definitely something we should keep an eye on, though we don't want to intervene too soon.